ARGUMENTUM

Matthias Jońca Isabellaque Leraczyk colloquuntur cum Petro Garnsey, professore emerito Cantabrigiensi, litterarum atque rerum gestarum scrutatore.

Problems concerning structures dynamics are being one of most important subjects in recent investigations associated with railways constructions. The need of modelling of such structures and their behaviour prediction leads to necessity of seeking new approaches, mainly due to highly increasing speeds of vehicles and traffic intensity. Comparative studies carried out on experimental data, measurements and theoretical research show that models based on multi-layered approach supported by semi-analytical approximations of solutions can give new insight into undertaken analyses. More detailed consideration of roads components and their physical properties, along with application of effective estimations allowing to avoid numerical instabilities linked with extremal dynamic variations, can be important tools in obtaining new solutions both, theoretical and engineering. This paper briefly presents a number of multilayer railway track models, with special emphasis on nonlinear track properties. Existing analytical and semi-analytical solution methods are presented with main advantages of new approaches. The theoretical double-beam system with two nonlinear layers is solved and computational examples are presented along with possibility of their transition to other multilayer structures analysis.

The study of the geometry for worm-gearing is much more complicated than that of plane gearing, since worm-gearing is three-dimensional. A numerical method to determine the conjugate profile of worm-gearing tooth is developed. The software, with numerical set-up and graphic display, is an original and special program, and it could be adopted for the geometry of any kind of cylindrical worm-gearings, as well as for spur gearings and bevel gearings.